Abstract: The potential energy expression of cylindrically symmetric intense electron beams is derived and the differential equation of RMS emittance is presented in this paper. The decrease of beam potential energy which is leaded by change of charged particle density distribution during the transportation brings the growth of RMS emittance. The change of the charged particle density distribution is always toward to decreasing the potential energy, such as the growth of the emittance. Furthermore, based on the basic definition of emttance, different model transverse motions including beam envelope oscillation with no influence on emittance and ruleless thermal motion with influence on emittance are expatiated. Several factors of influencing beam emittance are discussed respectively and some method